måndag 21 februari 2011

The Mystery of the 2nd Law Eliminated

One of the many common mysterious explanations of the concept of entropy as "measure of disorder". Very mysterious indeed, or do claim that you understand and can explain?

The 2nd Law of Thermodynamics has remained a mystery ever since it was formulated in the mid 19th century by Carnot, Clausius and Lord Kelvin.

The 2nd Law in its conventional formulation involves the concept of entropy S and the 2nd Law states that the entropy of a closed system can only increase in time, never decrease, that is
  • dS/dt > 0 (or dS/dt = 0)
where dS/dt is the time derivative of S.

The trouble with this formulation is that quantity denoted by S and named entropy, does not seem to have a well defined physical meaning as expressed by von Neumann to Shannon:
  • No one knows what entropy is, so if you in a debate use this concept, you will always have an advantage.
So the 2nd Law says that the entropy cannot decrease, but since "no one knows what entropy is", the statement of the 2nd Law is mysterious. Now, science based on mystery is not science, but all efforts to give entropy a clear physical meaning have failed.

The question then comes up if there is a formulation of the 2nd Law without the mysterious concept of entropy, a formulation involving only understood concepts?

Yes, there is an alternative formulation presented in the new book Computational Thermodynamics in terms of kinetic energy K, heat energy E, work W and turbulent dissipation D, which takes the following principal form without exterior forcing:
  • dK/dt = W − D,
  • dE/dt = − W + D,
  • D > 0,
where the condition D > 0 replaces the condition dS/dt > 0. The advantage of this formulation is that turbulent dissipation D with its sign D > 0 (or D = 0) is a physical concept which can be

We see that the 2nd Law expresses an irreversible transfer of kinetic energy into heat energy, while the total energy
  • TE = E + K
remains constant, as is seen by summing the two equations to get:
  • dTE/dt= dE/dt + dK/dt = 0.
We see that the work W transforms heat energy into kinetic energy or kinetic energy into heat energy depending on the sign of W:
  • In expansion with W positive, heat energy transforms into kinetic energy,
  • In compression with W negative, kinetic energy transforms into heat energy.
On the other hand, since D > 0 (or D = 0), turbulent dissipation can only transform kinetic energy into heat energy, and not heat energy into kinetic energy.

When you rub your hands they get warm, but you cannot get your hands rubbing by only heating them. Motion can generate heat by friction, but heat cannot generate motion by an inverse process of friction.

In the book you will discover a mathematical explanation of this familiar experience based on a concept of finite precision computation, which represents a new way of viewing physics as a form of analog computation of finite precision which can be simulated by digital computation.

So if you don't like to live with mysteries, take a look in the book see if you get the message.

If you want to get the message expressed in less technical form, you are invited to browse the
dialog between Mat and Phil in the likewise new book The Clock and the Arrow: A Brief Theory of Time exhibiting the connection between the 2nd Law and the Arrow of Time, that is why we get older and never younger.

9 kommentarer:

  1. Hej Claes

    När det gäller termodynamik och Maxwells demoner, andra huvudsatsen etc. ska du kolla in följande referenser. Då slipper du se entropi som oordning...

    [1] E.P. Gyftopoulos. Maxwell’s demon.(I) A thermodynamic exorcism. Physica A:
    Statistical Mechanics and its Applications, 307(3-4):405–420, 2002.

    [2] E.P. Gyftopoulos. Maxwell’s demon.(II) A quantum-theoretic exorcism. Physica A:
    Statistical Mechanics and its Applications, 307(3-4):421–436, 2002.

    [3] E.P. Gyftopoulos and E. Çubukçu. Entropy: thermodynamic definition and quantum
    expression. Physical Review E, 55(4):3851–3858, April 1997.

    [4] Elias P. Gyftopoulus. Entropy: An inherent, non-statistical property of any system in
    any state. International Journal of Thermodynamics, 9(3):107–115, September 2006.

    [5] G.N. Hatsopoulos. From Watt’s Steam Engine to the Unified Quantum Theory of
    Mechanics and Thermodynamics. International Journal of Thermodynamics, 9(3):97–
    105, September 2006.

    [6] G.N. Hatsopoulos and E.P. Gyftopoulos. A unified quantum theory of mechanics and
    thermodynamics. Part I. Postulates. Foundations of Physics, 6(1):15–31, 1976.

    [7] G.N. Hatsopoulos and E.P. Gyftopoulos. A unified quantum theory of mechanics and
    thermodynamics. Part IIa. Available energy. Foundations of Physics, 6(2):127–141,

    [8] G.N. Hatsopoulos and E.P. Gyftopoulos. A unified quantum theory of mechanics
    and thermodynamics. Part IIb. Stable equilibrium states. Foundations of Physics,
    6(4):439–455, 1976.

    [9] G.N. Hatsopoulos and E.P. Gyftopoulos. A unified quantum theory of mechanics and
    thermodynamics. Part III. Irreducible quantal dispersions. Foundations of Physics,
    6(5):561–570, 1976.

  2. Verkar vara statistik, och det är det jag inte förstår och vill ersätta med nåt begripligt.

  3. Hej Claes - Det är precis det som dessa författare oxå vänder sig emot. De gillar inte att se entropi som en statistisk företeelse. Jag tror att du kommer att gilla artiklarna. Se till exempel titeln på referens 4!!! Referens 5 är en bra översikt av vad de har gjort i sina tidiga papers och jag tycker att du ska börja med den.

  4. I would like to address the fact that the gentlemen at MIT have already developed a mathematically robust, NON-STATISTICAL model called “Quantum thermodynamics”. This is a controversial theory and I will not address the validity of their theory but I think you could benefit from visiting their website for more information on this subject, www.quantumthermodynamics.org/.

  5. Well, to go to QM to find a 2nd Law and irreversibility does not appeal to me, since it is like trying to understand a human being by studying one singe cell as if the apparent mystery of a persons actions could be found there.

  6. They don't go to quantum mechanics for the definition of entropy. The QM is only used since a theory of thermodynamics and thus the second law of thermodynamics should be valid everywhere. The only way to get rid of statistical mechanics is to make sure that ones formulation of the second law also is valid for small QM. The theory therefore might look a bit "theoretical" but the theory is beautifully presented in their book "Thermodynamics: Foundation and applications".

  7. Yes, it looks very "theoretical", not my cup of tea.

  8. Claes,
    Did you watch this video on the subject of time?

    "Is the Past Fixed? Part I"